Find the attached papers regarding Price convergence vs Market integration. I hope it will help you.

http://econ.upm.edu.my/ijem/vol2no2/bab08.pdf

http://www.econ.yale.edu/~pg87/convp.pdf

Thanks Mr. Abdul. Will go through and let's discuss.

I think that there is no unique answer. You probably expect market integration going along with price convergence. Before market integration of EU countries they had higher price difference across countries for the same commodity than today. But there are many counter-examples.

 Consider a digital platform booking.com . It allows to search over a million of hotels worldwide by any consumer. This is a typical example of market integration. However, we do not observe price convergence. Moreover, each user can get his special discount not applicable to other users. High complexity of information processing does not allow for price convergence. Price differentiation across consumers can be optimal policy for some hotels.

The similar platforms exist for air tickets, and price pattern for the same flight is very heterogeneous. For example, they sell first 10 tickets for only 50 euro, then next 20 for 100, but the last ticket can be sold for 300.

Another example is from simple commodity - natural gas. Here even in globalization we have regional prices, because of too high transport costs. This is opposite to the market for oil with unique price (Brent, for example) that depends only on time. About regional gas markets you can see the paper: https://www.researchgate.net/publication/289531408_Arbitrage_in_natural_gas_markets

Article Arbitrage in natural gas markets?

Article Price Convergence and Market Integration in China

http://econ.upm.edu.my/ijem/vol2no2/bab08.pdf

http://eel.my100megs.com/EEL_files/Vol5No1_files/EEL0512.pdf

http://www.econ.yale.edu/~pg87/convp.pdf

https://mpra.ub.uni-muenchen.de/40408/

https://core.ac.uk/download/pdf/6387312.pdf